Allardyce had been involved in talks two weeks ago after Ronald Koeman was sacked, but an agreement could not be reached.

But after Everton failed with their efforts to land Watford boss Marco Silva and endured a run of five defeats in seven games under interim boss David Unsworth, they have returned to Allardyce's representatives within the last 48 hours.

Caretaker Everton boss David Unsworth reflects on his position after the Southampton defeat

Caretaker Everton boss David Unsworth reflects on his position after the Southampton defeat

And one source has told Sky Sports News that progress has been made on the key aspect of the length of the 63-year-old's contract.

It is also understood that Shakhtar Donetsk manager Paulo Fonseca has also been interviewed for the role, while Republic of Ireland's Martin O'Neill is also being considered.

Majority shareholder Farhad Moshiri is the person leading the search but has yet to make his final decision, which is expected on Tuesday.

Allardyce was initially offered a deal until the end of the season and, after pulling out of discussions, said he did not feel wanted enough by the club, and was put off by their indecision.

Allardyce has been the preferred choice of Everton director of football Steve Walsh but Moshiri has, until now, had other ideas.

Sam Allardyce recently discussed his future with Sky Sports

Sam Allardyce recently discussed his future with Sky Sports

Should Allardyce be appointed, Sky Sports News understands he is also likely to be joined by another former Leicester employee in Craig Shakespeare, who was his right-hand man during the ill-fated four-month spell with England.

Allardyce's last job was at Crystal Palace, whom he left in May after saving them from relegation, but he was keen to take a break from management and had no ambitions for another job.

Everton had wanted to appoint Watford boss Marco Silva

Palace chairman Steve Parish agreed to his departure and it is believed the south London club would receive a compensation package of around £2m if Allardyce took a new job before next summer.

Sky Sports News understands that Allardyce is currently on holiday in Dubai, having enjoyed a trip to the Abu Dhabi Grand Prix over the weekend.